Properties

Base field \(\Q(\sqrt{15}) \)
Label 2.2.60.1-50.1-g
Conductor 50.1
Rank not recorded

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Base field \(\Q(\sqrt{15}) \)

Generator \(a\), with minimal polynomial \( x^{2} - 15 \); class number \(2\).

Elliptic curves in class 50.1-g over \(\Q(\sqrt{15}) \)

Isogeny class 50.1-g contains 4 curves linked by isogenies of degrees dividing 15.

Curve label Weierstrass Coefficients
50.1-g1 \( \bigl[1\) , \( 0\) , \( 1\) , \( -126\) , \( -552\bigr] \)
50.1-g2 \( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( 97 a - 376\) , \( -1161 a + 4498\bigr] \)
50.1-g3 \( \bigl[1\) , \( 0\) , \( 1\) , \( -1\) , \( -2\bigr] \)
50.1-g4 \( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( -703 a + 2724\) , \( 8579 a - 33222\bigr] \)

Rank

Rank not yet determined.

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 15 & 3 & 5 \\ 15 & 1 & 5 & 3 \\ 3 & 5 & 1 & 15 \\ 5 & 3 & 15 & 1 \end{array}\right)\)

Isogeny graph